Simple proof of fault tolerance in the graph-state model

Abstract

We consider the problem of fault tolerance in the graph-state model of quantum computation. Using the notion of composable simulations, we provide a simple proof for the existence of an accuracy threshold for graph-state computation by invoking the threshold theorem derived for quantum circuit computation. Lower bounds for the threshold in the graph-state model are then obtained from known bounds in the circuit model under the same noise process.

6 pages, 2 figures, REVTeX4. (v4): Minor revisions and new title; published version

References in corpus (13)

• Measurement-based quantum computation with cluster states
• Quantum Computing with Very Noisy Devices
• Resource-efficient linear optical quantum computation
• Optical quantum computation using cluster states
• Overhead and noise threshold of fault-tolerant quantum error correction
• Resilient Quantum Computation: Error Models and Thresholds
• Valence Bond Solids for Quantum Computation
• Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Fault-tolerant quantum computation with cluster states
• Unified derivations of measurement-based schemes for quantum computation
• Noise thresholds for optical quantum computers
• Computation by measurements: a unifying picture

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